Quantum transport reveals spin glass correlations in a 2D network of TbPc$_{2}$ single-molecule magnets grafted on graphene

Abstract

The low temperature magnetoresistance of graphene functionalized by an array of magnetic Terbium Phthalocyanines molecules is found to exhibit a magnetic field-dependent 1/f noise, along with universal conductance fluctuations (UCFs) typical of a mesoscopic phase-coherent sample. A thorough analysis of the magnetic field, temperature and chemical potential dependence of this 1/f noise and UCFs reveals that long range, 2D Ising spin-glass like, magnetic correlations are induced in graphene through exchange interactions between the magnetic molecules and charge carriers in graphene. These experiments show that graphene functionalized with organic molecules constitutes a versatile platform for the investigation of magnetic phase transitions in two dimensions.

Figures (14)

• Figure 1: Schematic representation of the two types of graphene field effect transistors coated with 10$^{-5}$ M concentration TbPc$_{2}$T layers deposited on graphene by the drop casting method. (a) Pure monolayer graphene (b) Monolayer graphene and WS$_{2}$ heterostructure. (c) and (d): Gate voltage dependence of the resistance of samples shown in (a) and (b).
• Figure 2: Low-temperature magnetoconductance $\delta G=G(B)-G(0)$, in units of $e^2/h$, of three samples. $G(B)$ plain lines and $G(-B)$ dotted lines are plotted on the same graphs to emphasize the field asymmetry in the TbPc$_{2}$-coated device : (a) and (b) graphene sample coated by a monolayer of Fe porphyrins, (c) and (d) sample coated by the dilute solution B of TbPc$_{2}$ molecules,( e) and (f) sample coated by the dense solution A of TbPc$_{2}$ molecules.
• Figure 3: Magneroresistance of the Graphene/TbPc$_{2}$ (a) and WS$_{2}$/Graphene/TbPc$_{2}$ (b) samples, both coated by the dense solution A of TbPc$_{2}$. $\delta R=R(B)-R0$, with $R0=R(B=0)$ The gate voltage is $V_g=$ 20 V. The out-of-plane field is varied between $\pm$3000 G. The electronic temperature is of the order of 50 mK. In both samples, an excess resistance noise is noticeable around zero field, between $\pm 0.1 T$.
• Figure 4: (a) Color-coded resistance of the Graphene/TbPc$_{2}$ sample at 20 V gate voltage, as a function of field and time. The field is swept from -0.3 T to +0.3 T, and at each field value 100 points are recorded, 1 every 2 s. (b) Field dependence of all the resistance values, in black, left scale, and average resistance $< R(B)>$, in red, right scale. (c) Standard deviation of the resistance as a function of magnetic field. d) Comparison of $<R(B)>$ and $<R(-B)>$, showing the field asymmetry of the time-averaged resistance .
• Figure 5: Standard deviation of the resistance (resp. conductance) fluctuations $\Delta R (B)$ for different temperatures, corresponding to the left (resp. right) axis. Upper panel G/TbPc$_2$ sample at $V_g=70 V$. Lower panel WS$_2$/G/TbPc$_2$ sample at $V_g=55 V$. The smooth lines are lorenzian fits of the data. (The curves have been shifted along the Y axis for clarity purposes.)